Mathological: Red Sox are Choking Edition

I'm not sure that I've coined a new term. Someone must have thought of it before. But here at BriWise, "Mathological" will now be used to refer to any attempt to mislead with numbers. It's part of my campaign for a more statistically aware planet. Yesterday was a topical attempt since I had been comparing job offers and was hoping to help others in the same boat. Today is a little more frivolous. As a Red Sox fan, current sports events just feel like history repeating itself. The Sox are choking again. They were up by 10 games at the All Star break and here it is, barely a month later and the lead is down to 4. It's inevitable that we implode and the Yankees overtake us, right?

Well, there's perception and then there is reality. Let's look at the numbers

W L Pct
Boston 71 47 0.602
NYY 67 51 0.568

Now, how have they performed since the Al-Star break?

W L Pct
Boston 18 13 0.580
NYY 24 08 0.750

Which of those percentages looks closest to the season average? At the break, the Sox would have been 53-34 for a percentage of 0.609 while the Yankees were 43-43, for a percentage of 0.500.

If we apply those percentages to what they have done since the break, we see that the expected value of Sox wins was 19. So, they are certainly close to the pace they were setting before the break. For those who don't want to do the math, 19/31 = 0.612. The Yankees, conversely, played a mediocre first half and only won half their games. That means, they should have been expected to win 16 games. They won a full 50% more.

Does this help us predict anything? Of course not! If it did, we wouldn't need to play the season. But it does suggest that the Sox are not choking. They have lost 4 of their last 7. So, the immediate impression is that they are doing poorly. The Yankees, on the other hand, have caught fire. They are not as bad as the data of the first 86 games suggests, but they are not as good as the data of the last 32 either. How do I know? Let's look at more numbers!

If a team was to play 0.750 ball for a season, they would win 121 games. That hasn't been done in the modern era, which is a fairly large sample size. So, while it is not impossible, it is statistically unlikely.

That doesn't mean the Yankees won't catch the Red Sox. With 44 games left, if the Sox continue playing with consistency, they will win 26 or 27 more games, falling a little shy of the coveted 100 win plateau. Let's say 26 for the sake of argument meaning they would end up with 97 wins. The Yankees need to win 31 of their remaining 44 to overtake the Sox, a winning percentage of 0.704. Not impossible, but, again, statistically unlikely.

This isn't meant to cheer anybody up. Just a little numerical reminder that the Sox are not choking. The Yanks are surging. So, lay off and stop stressing all you doom and gloomers!